This paper is devoted to some inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions in boundary vertices. By making use of Rouché's theorem, we derive the eigenvalue asymptotics of these operators. Besides, we show that for each of these operators, if the potentials are known a priori for all but one edge on the graph, then the potential on the remaining edge is uniquely determined by part of the potential on this edge and part of its spectrum. Our method relies upon some estimates of infinite products given by Horváth.

中文翻译：

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混合边界条件星图上狄拉克算子的逆谱问题

本文致力于研究在边界顶点具有混合边界条件的星形图上狄拉克算子的一些逆谱问题。利用Rouché 定理，我们推导出这些算子的特征值渐近。此外，我们表明，对于这些算子中的每一个，如果图上除一条边之外的所有边的电位都是先验已知的，那么剩余边上的电位由这条边上的部分电位及其频谱的一部分唯一确定. 我们的方法依赖于 Horváth 给出的无限乘积的一些估计。